Two thousand four hundred years ago Socrates gave a remarkable lesson of geometry, perhaps the first detailed record of a pedagogical method in vivo in history [Plato. (2008). "Apologia de Socrates. Menon. Cratilo." Madrid: Alianza Editorial]. Socrates asked Meno's slave 50 questions requiring simple additions or multiplications. At the…

This report discusses four different types of instruction which enable learning disabled or low achieving students to learn well enough to transfer the skill to a novel situation. After asserting that generalization depends on systematic instruction, the paper describes the four procedures: (1) teacher-directed generalization; (2) direct…

Discussed are generalizations and problem solving, unsound uses of generalizations, generalization as data, and student discovery of generalizations. (CT)

Using mathematics as an example, the nature of the confusion between "knowledge" and "coming to know" is elucidated. The range of curriculum choices available to structuralists once the distinction is clarified is larger, and teaching a body of knowledge and teaching by discovery are compatible. (Author/MLF)

This study was conducted to determine if use of discovery methods (multiple-choice generalization or written generalization) would have differential effects on mathematics achievement and attitudes of college students in remedial mathematics. No significant difference between the two was found. (MNS)

This study compared discovery and expository methods of teaching lip-reading skills to 26 college students with normal hearing. No significant differences were found in method effectiveness. Training in consonant-vowel syllables was somewhat maintained four weeks later but did not generalize to word identification skills. (Author/DB)

Presents methods for teaching two mathematical concepts that utilize visualization. The first illustrates a visual approach to developing the formula for the sum of the terms of an arithmetic sequence. The second develops the relationship between the slopes of perpendicular lines by performing a rotation of the coordinate axes and examining the…

Offers calculus students and teachers the opportunity to motivate and discover the first Fundamental Theorem of Calculus (FTC) in an experimental, experiential, inductive, intuitive, vernacular-based manner. Starting from the observation that a distance traveled at a constant speed corresponds to the area inside a rectangle, the FTC is discovered,…

Evaluation of a sequenced inquiry learning task with 20 normally achieving junior high students, 18 students with learning disabilities (LD), and 16 with mild mental retardation (MR) found 75 percent of the normal, 50 percent of the LD, but none of the MR students made the correct induction. LD and MR students were less likely to answer…

Teachers and teacher educators seem to be little aware of some major concepts about instruction that provide important insights into the central requirements for learning. A common misconception is that motivation has to do with wanting or desiring. It is instead attention to stimuli that is influenced by two powerful agents--(1) suspense,…

Chess experts remember meaningful knowledge in the form of networks or patterns. Applied to mathematics instruction, effective classroom approaches can use investigation to identify patterns or rules. Described are a class activity and a small-group activity to investigate addition of signed numbers and linear relationships. (MDH)